Question

in a Vernier caliper vernier scale division is x cm and n divisions of vernier scale coincide with n-1 divisions of main scale the least count in the caliper in centimetres is

Answer 1

the least count of vernier = length of each division on main scale / number of division on vernier scale

least count =x/n

Answer 2

Answer:  

The least count is $\bold{\frac{x}{n} \mathrm{cm}}$.

Solution:

The least count of Vernier can be calculated by dividing the length of each division on main scale with number of divisions in ‘Vernier scale’.

$L.C.=\frac{\text { Length of each division in main scale}}{\text {Number of divisions on vernier scale}}=1 M S D-1 V S D$

Here MSD is “main scale division” and VSD is “Vernier scale division”.

As it is given that n division of Vernier scale “coincide with (n-1) divisions” of main scale, we get

$n V S D=(n-1) M S D$

$1 V S D=\frac{(n-1)}{n} M S D$

We know that

$L.C.=1 M S D-1 V S D=1 M S D-\left(\frac{n-1}{n}\right) M S D$

$L . C=1 M S D-1 M S D+\frac{1}{n} M S D$

Thus, least count of Vernier scale is $\frac{1}{n} \mathrm{MSD}$. As it is said the length of each division is x cm in Vernier scale, so the least count will be $x \times \frac{1}{n} \mathrm{cm}.$ Thus the least count of ‘Vernier caliper’ will be $\frac{x}{n} \mathrm{cm}$.